How do you graph 6x>=-1/3y on the coordinate plane?

Jun 30, 2018

See explanation

Explanation:

Given: $6 x \ge - \frac{1}{3} y$

Multiply both sides by (-1 )

$- 6 x \le \frac{1}{3} y \textcolor{w h i t e}{\text{dd}}$ Notice that the inequality has turned round.

Multiply both sides by 3

$- 18 x \le y$

Now plot the straight line graph of $y = - 18 x$

Draw any vertical line. $y$ can and may take on any value above and on $y = - 18 x$

Example: suppose I pick on $x = \frac{1}{2}$ Then the brown line in the graph below represents all the feasible values for $y$ at $x = \frac{1}{2}$

Lots and lots of these lines, when combined, give an 'area' on the graph (as shaded) that represents all the possible values of $y$ for all the possible values of $x$.